Aerospace vehicle navigation and control system comprising terrestrial illumination matching module for determining aerospace vehicle position and attitude

ABSTRACT

The present invention relates to an aerospace vehicle navigation and control system comprising a terrestrial illumination matching module for determining spacecraft position and attitude. The method permits aerospace vehicle position and attitude determinations using terrestrial lights using an Earth-pointing camera without the need of a dedicated sensor to track stars, the sun, or the horizon. Thus, a module for making such determinations can easily and inexpensively be made onboard an aerospace vehicle if an Earth-pointing sensor, such as a camera, is present.

RIGHTS OF THE GOVERNMENT

The invention described herein may be manufactured and used by or forthe Government of the United States for all governmental purposeswithout the payment of any royalty.

FIELD OF THE INVENTION

The present invention relates to an aerospace vehicle navigation andcontrol system comprising a terrestrial illumination matching module fordetermining aerospace vehicle position and attitude.

BACKGROUND OF THE INVENTION

Aerospace vehicle's need to periodically determine their position withrespect to the Earth so they can stay on their flight path or orbit. Inorder to determine such position, an aerospace vehicle must be able todetermine its pose estimation between two points in time and/or attitudewith respect to the Earth. Currently, aerospace vehicles such assatellites primarily use star trackers to determine their orbitalposition. The manner in which other aerospace vehicles determine theirposition with respect to the earth is found in Table 1. All of thecurrent methods of determining an aerospace vehicle's position withrespect to the earth cannot determine pose estimation between two pointsin time and/or attitude through one sensor and such sensors must bededicated sensors. As dedicated sensors are required, the aerospacevehicle requires additional mission specific sensors that add undesiredbulk and weight. Furthermore, the further away from the earth that theaerospace is positioned, the more difficult the task of determining suchaerospace's position with respect to the earth becomes.

Applicants recognized that the source of the problems associated withcurrent methods lie in the use of complex inputs such as starlight thatrequire that sensors which are positioned such that they cannot focus onthe earth. In view of such recognition, Applicants discovered that earthlight, such the light emitted by cities, could substitute for starlight.Thus, sensors that are mission specific that are focused on the earthcould be dual use sensors that acquire mission specific information andinformation for determining an aerospace vehicle's position. As aresult, the bulk and weight of an aerospace vehicle can be significantlyreduced. In addition, to the aforementioned benefits, Applicantsaerospace vehicle navigation and control system can serve as a backupnavigation and control system for any conventional system thus obviatingthe need for other backup navigation systems that would inherentlyintroduce unwanted bulk and weight to the subject aerospace vehicle.

SUMMARY OF THE INVENTION

The present invention relates to an aerospace vehicle navigation andcontrol system comprising a terrestrial illumination matching module fordetermining spacecraft position and attitude. The method permitsaerospace vehicle position and attitude determinations using terrestriallights using an Earth-pointing camera without the need of a dedicatedsensor to track stars, the sun, or the horizon. Thus, a module formaking such determinations can easily and inexpensively be made onboardan aerospace vehicle if an Earth-pointing, sensor such as a camera ispresent.

Additional objects, advantages, and novel features of the invention willbe set forth in part in the description which follows, and in part willbecome apparent to those skilled in the art upon examination of thefollowing or may be learned by practice of the invention. The objectsand advantages of the invention may be realized and attained by means ofthe instrumentalities and combinations particularly pointed out in theappended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate embodiments of the presentinvention and, together with a general description of the inventiongiven above, and the detailed description of the embodiments givenbelow, serve to explain the principles of the present invention.

FIG. 2A presents the first mode of operation for the module, which givesthe aerospace vehicle's pose following the processing of terrestriallight images.

FIG. 2B presents the second mode of operation for the module, whichgives the aerospace vehicle's attitude following the processing ofterrestrial light images.

FIG. 1 is the hardware system schematic and block diagram comprising theterrestrial illumination matching (TIM) module, a camera and/or othersensor which generates terrestrial light images, an onboard centralprocessing unit (CPU), and vehicle actuators.

It should be understood that the appended drawings are not necessarilyto scale, presenting a somewhat simplified representation of variousfeatures illustrative of the basic principles of the invention. Thespecific design features of the sequence of operations as disclosedherein, including, for example, specific dimensions, orientations,locations, and shapes of various illustrated components, will bedetermined in part by the particular intended application and useenvironment. Certain features of the illustrated embodiments have beenenlarged or distorted relative to others to facilitate visualization andclear understanding. In particular, thin features may be thickened, forexample, for clarity or illustration.

DETAILED DESCRIPTION OF THE INVENTION

Definitions

Unless specifically stated otherwise, as used herein, the terms “a”,“an” and “the” mean “at least one”.

As used herein, the terms “include”, “includes” and “including” aremeant to be non-limiting.

It should be understood that every maximum numerical limitation giventhroughout this specification includes every lower numerical limitation,as if such lower numerical limitations were expressly written herein.Every minimum numerical limitation given throughout this specificationwill include every higher numerical limitation, as if such highernumerical limitations were expressly written herein. Every numericalrange given throughout this specification will include every narrowernumerical range that falls within such broader numerical range, as ifsuch narrower numerical ranges were all expressly written herein.

Evening Civil Twilight is the period that begins at sunset and ends inthe evening when the center of the sun's disk is six degrees below thehorizon. Morning Civil Twilight begins prior to sunrise when the centerof the sun's disk is six degrees below the horizon, and ends at sunrise.The most recent version of the Air Almanac as published by the U.S.government should be used to as the source of the sun's position on theday in question.

Nomenclature, Subscripts and Background

-   -   a=semi-major radius    -   b=semi-minor radius    -   C=attitude matrix    -   e=eccentricity    -   ê=unit vector of s    -   E=Essential Matrix    -   e²=square of first eccentricity    -   f=flattening of the planet    -   ƒ=process nonlinear vector function    -   F=matrix of linearized dynamics    -   F=Fundamental matrix    -   f_(c)=focal length of camera    -   g=gravitational acceleration    -   H=Jacobian of measurement sensitivity    -   h=observation function    -   h_(E)=height of vehicle above Earth's surface    -   I=identity matrix    -   JD=Julian Day    -   K=Kalman gain    -   k=equatorial gravity constant    -   N=radius of curvature of vertical prime    -   n=integer number    -   P=covariance of state    -   Q=process noise covariance matrix    -   q₀=equatorial gravity    -   R=measurement noise covariance matrix    -   R=rotation matrix between coordinate frames    -   r=vehicle position    -   s=measurement from camera to point on earth    -   T=pose matrix    -   t=translation    -   t=time    -   u=input vector    -   v=vehicle velocity    -   w=measurement noise    -   W=weights    -   x=state vector    -   X=image coordinate    -   y=measurement    -   Y=expected measurement    -   β=reduced latitude    -   T=residuals of observations    -   Δ=change or nutation    -   ε=obliquity of the ecliptic    -   θ=Greenwich Apparent Sidereal Time    -   κ=filter tuning value    -   μ=gravitational parameter    -   σ=accuracy of sensor    -   ν=residual    -   φ=latitude, deg    -   χ=set of sigma points    -   ψ=longitude    -   ω=angular rate        Super/Subscripts    -   −=state a priori, but after propagation    -   +=state a posteriori    -   0=initial state    -   c=integer number    -   CAM=camera frame    -   E=conditions for the Earth    -   ECEF=measured with respect to a rotating frame    -   ECI=measured with respect to an inertial frame    -   gc=geocentric    -   gd=geodetic    -   I=inertial    -   i=integer index    -   k=timestep    -   m=integer number    -   m=mean    -   n=integer number    -   n=normalized    -   xx=predicted mean covariance    -   xy=predicted cross covariance    -   yy=predicted observed covariance        Kalman Filters

Kalman Filter (KF), an Extended Kalman Filter (EKF) and/or an UnscentedKalman Filter (UKF) are used to propagate a state vector and update witha measurement. Typically, the accuracy of said aerospace vehicle'spropagated position and/or attitude is best if an Unscented KalmanFilter is used, with the next best filter being an Extended KalmanFilter and/or a Kalman Filter. Suitable of applying such filters arepresented below.

Kalman Filter: Given the system dynamics along with x_(k) ⁻, P_(k) ⁻,y_(k), Q_(k), and R_(k) the Kalman Gain is calculated as follows:K _(k) =P _(k) ⁻ H ^(T)(HP _(k) ⁻ H ^(T) +R)⁻¹The current state estimate is{circumflex over (x)} _(k) ⁺ ={circumflex over (x)} _(k) ⁻ +K _(k)(y_(k) −H{circumflex over (x)} _(k) ⁻)and the current covarianceP _(k) ⁺ =P _(k) ⁻ −K _(k) HP _(k) ⁻

The system is then propagated from k to k+1 with{circumflex over (x)} _(k+1) ⁻=ƒ({circumflex over (x)} _(k) ⁺ ,t)

${F(t)} = \left. \frac{\partial{f\left( {x,t} \right)}}{\partial x} \right|_{x = \overset{.}{x}}$andP _(k+1) ⁻ =FP _(k) ⁺ F ^(T) +Q _(k)

Extended Kalman Filter: The position estimator will rely on the use ofan EKF based on its use in contemporary literature, as well as thespecific application using the camera frame. Attempting to write theprocess in sequential order for an EKF, it is formulated by firstdefining the system dynamics as{dot over (x)}=ƒ(x,t)and the covariance matrix, P, is able to be propagated by{dot over (P)}=FP+PF ^(T) +Qwhere

${F(t)} = \left. \frac{\partial{f\left( {x,t} \right)}}{\partial x} \right|_{({x = x^{*}})}$and Q is the process noise. It is evaluated at the expected values ofthe state dynamics. The measurement y, is related to the state vector bythe relationy=h(x,t)

Letting H be the Jacobian of this relationship, also known as themeasurement sensitivity matrix,

$H = \left. \frac{\partial h}{\partial x} \right|_{({x = x^{*}})}$

This is found using the Line of Sight measurements by using the Inertialto Camera frame, and the dot product of the unit vectors in the inertialframe

$H_{k} = {R_{CAM}^{ECI}{\frac{1}{\left. ||s_{k} \right.||}\left\lbrack {\left\{ {{ê_{k}^{ECI}ê_{k}^{ECI^{T}}} - I_{3x3}} \right\} 0_{3x3}} \right\rbrack}}$

R_(CAM) ¹ is found by assuming the attitude at the time the image wastaken is known. At this point the measurement noise covariance is neededand determined asR=σ ²(I _(3×3) −ē _(k) ^(CAM) e _(k) ^(CAM) ^(T) )

For the Kalman Gain and using the measurement, determine the residual tobev _(k) =y _(k) −h(x _(k) ,t _(k))

The Kalman gain for the system can be calculated asK _(k) =P _(k) ⁻ H _(k) ^(T)(H _(k) P _(k) ⁻ H _(k) ^(T) +R _(k))⁻¹where P is the expected mean squared error and R is the knowncovariance.

The current state estimate can be updated using this gain and theresidual{circumflex over (x)} _(k) ⁺ ={circumflex over (x)} _(k) ⁻ +K _(k)(y_(k) −H _(k) {circumflex over (x)} _(k) ⁻)

The current covariance must also be updated asP _(k) ⁺ =P _(k) ⁻ −K _(k) H _(k) P _(k) ⁻

Unscented Kalman Filter: An Unscented Kalman filter is the preferredtype of filter to use for nonlinear discrete time systems. The equationsfor an Unscented Kalman Filter arex _(k+1) =f(x _(k) ,u _(k) ,v _(k) ,k),y _(k) =h(x _(k) ,u _(k) ,k)+w_(k)

A set of points (sigma points, χ) are deterministically selected suchthat their mean and covariance match that of the state. There are 2n+1sigma points and associated weights; points are chosen in the classicUKF to match first two moments.χ^(m) =x ,

$W_{0} = \frac{\kappa}{n + \kappa}$χ_(i) ^(m) =x +(√{square root over ((n+κ)P _(xx))})_(i),

$W_{i} = \frac{1}{2\left( {n + \kappa} \right)}$χ_(i+n) ^(m) =x −(√{square root over ((n+κ)P _(xx))})_(i),

$W_{i + n} = \frac{1}{2\left( n_{k} \right)}$

Each sigma point is propagated throughχ_(k|k−1) ^((i)) =f(χ_(k−1) ^((i)))which are averaged to find a predicted mean, used to compute acovariance

$P_{{xx},k}^{-} = {{\sum\limits_{i = 0}^{2n}{{W_{i}^{c}\left( {\chi_{k❘{k - 1}}^{i} - {\hat{\overset{\_}{x}}}_{k}^{-}} \right)}\left( {\chi_{k❘{k - 1}}^{i} - {\hat{\overset{\_}{x}}}_{k}^{-}} \right)^{T}}} + Q_{k - 1}}$

Now consider residual information, and transform the sigma points toobservationsΓ_(k|k−1) ^((i)) =h(χ_(k|k−1) ^((i)))

Average the transformed sigma points to determine an expectedmeasurement

${\hat{Y}}_{k} = {\sum\limits_{i = 0}^{2n}{W_{i}^{m}\Gamma_{k❘{k - 1}}^{(i)}}}$

Having an expected measurement, the predicted observation covariance canbe determined

$P_{{yy},k} = {{\sum\limits_{i = 0}^{2n}{{W_{i}^{c}\left( {\Gamma_{k❘{k - 1}}^{(i)} - {\hat{Y}}_{k}^{-}} \right)}\left( {\Gamma_{k❘{k - 1}}^{(i)} - {\hat{Y}}_{k}^{-}} \right)^{T}}} + R_{k}}$as well as the predicted cross covariance

$P_{{xy},k} = {\sum\limits_{i = 0}^{2n}{{W_{i}^{c}\left( {\chi_{k❘{k - 1}}^{i} - {\hat{\overset{\_}{x}}}_{k}^{-}} \right)}\left( {\Gamma_{k❘{k - 1}}^{(i)} - {\hat{Y}}_{k}^{-}} \right)^{T}}}$

Finally, the standard Kalman filter update can be appliedν=Y−Ŷ _(k)K _(k) =P _(xy) P _(yy) ⁻¹{circumflex over ( x )}_(k) ⁺={circumflex over ( x )}_(k) ⁻ +K _(k)νP _(xx,k) ⁺ =P _(xx,k) ⁻ −K _(y) P _(yy) K _(k) ^(T)

TABLE 1 Aerospace Vehicle Type and Modes of Guidance, Navigation, andControl Vehicle GNC Methods Maneuver Method AIR Weather Balloonradiosonde, theodolite pressure inside balloon Manned aircraftaltimeter, inertial navigation thrust, flight control system (INS),Global surfaces Positioning System (GPS) Unmanned aircraft altimeter,INS, GPS thrust, flight control surfaces Quadcopter visual sensor, GPSpropeller(s) Airborne Missile altimeter, INS, GPS thrust, flight controlsurfaces AEROSPACE Scientific Balloon star camera, altimeter pressureinside balloon Sounding Rocket ring laser gyro, altimeter, thrust,flight control accelerometers surfaces Space Shuttle human-in-the-loop,thrust, flight control star camera surfaces Launch Vehicle INS, ringlaser gyro, thrust, flight control (Rocket) altimeter, accelerometerssurfaces Ballistic Missile INS, GPS thrust, flight control surfacesSPACE Satellite star camera, sun sensor, thruster, electric horizonsensor, GPS propulsion, magnetorquer, momentum wheel Space Stationhuman, star camera, sun thruster, electric sensor, horizon sensor,propulsion, GPS magnetorquer, momentum wheel Interplanetary star camera,sun sensor thruster, electric Vehicle propulsion, momentum wheelExamples of Flight Control Surfaces: Fins, Ailerons, Elevators. Thrustincludes the two-directional thrust force, as well as any gimbaledthrust vectoring the vehicle is capable of generating.Method of Determining an Aerospace Vehicle's Position

Applicants disclose a method of determining an aerospace vehicle'sposition with respect to the Earth, determining the aerospace vehicle'spose estimation between two points in time and/or attitude with respectto the Earth wherein:

-   -   a) determining an aerospace vehicle's position with respect to        the Earth comprises:        -   (i) having an aerospace vehicle acquire, at a time from            Evening Civil Twilight to Morning Civil Twilight, an image            of the Earth comprising at least one terrestrial light            feature;        -   (ii) matching said least one terrestrial light feature of            the image with at least one feature of a terrestrial light            data base;        -   (iii) weighting said matched images;        -   (iv) optionally, calculating the aerospace vehicle's            propagated position and checking the result of said            propagated position against the weighting;        -   (v) using the time and altitude that said image was taken to            convert said weighted match into inertial coordinates;        -   (vi) optionally updating said aerospace vehicle's propagated            position by using the inertial coordinates in a propagation            position and/or attitude calculation; and/or    -   b) determining the aerospace vehicle's pose estimation between        two points in time comprising:        -   (i) having an aerospace vehicle acquire, at a time from            Evening Civil Twilight to Morning Civil Twilight, at least            two images of the Earth at different times, each of said            images containing at least one common terrestrial light            feature;        -   (ii) comparing said two images to find at least one common            terrestrial light feature;        -   (iii) calculating the pose as follows:            -   converting the image's camera coordinates to normalized                coordinates;            -   calculating an essential matrix from the normalized                coordinates and then recovering the pose from the                essential matrix; or            -   converting the image's camera coordinates to normalized                coordinates;            -   converting the normalized coordinates to pixel                coordinates;            -   calculating a fundamental matrix from the pixel                coordinates and then recovering the pose;        -   (iv) combining a known absolute position and attitude of the            aerospace vehicle with the recovered pose to yield an            updated attitude and an estimated position for the aerospace            vehicle.

Applicants disclose a method of determining an aerospace vehicle'sposition with respect to the Earth, determining the aerospace vehicle'spose estimation between two points in time and/or attitude with respectto the Earth wherein:

-   -   a) determining an aerospace vehicle's position with respect to        the Earth comprises:        -   (i) having an aerospace vehicle acquire, at a known general            altitude and at time from Evening Civil Twilight to Morning            Civil Twilight, an image of the Earth comprising at least            one terrestrial light feature;        -   (ii) matching, using Lowe's ratio test, said least one            terrestrial light feature of the image with at least one            feature of a terrestrial light data base;        -   (iii) weighting, to a scale of one, said matched images;        -   (iv) optionally, calculating the aerospace vehicle's            propagated position, using a Kalman Filter, an Extended            Kalman Filter and/or an Unscented Kalman Filter, (typically            the accuracy of said aerospace vehicle's propagated position            and/or attitude is best if an Unscented Kalman Filter is            used, with the next best filter being an Extended Kalman            Filter) and checking the result of said propagated position            against the weighting;        -   (v) using the time and altitude that said image was taken at            to convert said weighted match into inertial coordinates by            transforming a state vector containing position and velocity            from Earth-Centered-Earth-Fixed (ECEF) coordinates to            Earth-Centered-Inertial (ECI) coordinates using the            following equations:            r ^(ECI) =Rr ^(ECEF)            v ^(ELI) =Rv ^(ECEF) +{dot over (R)}r ^(ECEF)

$R = \begin{bmatrix}{{- \sin}\theta} & {{- \cos}\theta} & 0 \\{\cos\theta} & {{- \sin}\theta} & 0 \\0 & 0 & 0\end{bmatrix}${dot over (R)}=ω _(E) R

-   -   -   -   where θ represents the Greenwich Apparent Sidereal Time,                measured in degrees and computed as follows:                θ=[θ_(m)+Δψ cos(ε_(m)+Δε)])·mod(360°)            -   where the Greenwich mean sidereal time is calculated as                follows:                θ_(m)=100.46061837+(36000.770053608)t+(0.000387933)t                ²−(1/38710000)t ³            -   where t represents the Terrestrial Time, expressed in                24-hour periods and the Julian Day (JD):

$t = \frac{{JD} - {2000{January}01^{d}12^{h}}}{36525}$

-   -   -   -   wherein the mean obliquity of the ecliptic is determined                from:                ε_(m)=23°26′21.″448−(46.″8150)t−(0.0″00059)t                ²+(0.″001813)t ³            -   wherein the nutations in obliquity and longitude involve                the following three trigonometric arguments:                L=280.4665+(36000.7698)t                L′=218.3165+(481267.8813)t                Ω=125.04452−(1934.136261)t            -   and, the nutations are calculated using the following                equations:                Δψ=−17.20 sin Ω−1.32 sin(2L)−0.23 sin(2L′)+0.21 sin(2Ω)                Δε=9.20 cos Ω+0.57 cos(2L)+0.10 cos(2L′)−0.09 cos(2Ω)            -   then using, the equations for the position, r, and                velocity, v, in the ECI frame to calculate the position                and velocity in the ECEF frame using the dimensions of                the earth, preferably the following dimensions for the                Earth are used:                a=6378137m                b=6356752.3142m                q ₀=9.7803267714m/s ²                k=0.00193185138639                e ²=0.00669437999013            -   when longitude is calculated from the ECEF position by:

$\psi = {\arctan\left\lbrack \frac{r_{y}^{ECEF}}{r_{x}^{ECEF}} \right\rbrack}$

-   -   -   -   The geodetic latitude, φ_(gd), is calculated using                Bowring's method:

$\overset{\_}{\beta} = {\arctan\left\lbrack \frac{r_{z}^{ECEF}}{\left( {1 - f} \right)s} \right\rbrack}$

$\varphi_{gd} = {\arctan\left\lbrack \frac{r_{z}^{ECEF} + {\frac{e^{2}\left( {1 - f} \right)}{\left( {1 - e^{2}} \right)}R\sin^{3}\beta}}{s - {e^{2}R\cos^{3}\beta}} \right\rbrack}$

-   -   -   -   finally the geocentric latitude is calculated from the                geodetic,

${\tan\varphi_{gd}} = {\frac{\left( {\frac{a_{e}\left( {1 - e^{2}} \right)}{\sqrt{1 - {e^{2}\sin^{2}\varphi_{gd}}}} + h_{gd}} \right)}{\left( {\frac{a_{e}}{\sqrt{1 - {e^{2}\sin^{2}\varphi_{gd}}}} + h_{gd}} \right)}\tan\varphi_{gd}}$

-   -   -   -   where f is the flattening of the planet; e² is the                square of the first eccentricity, or e²=1−(1−f)²; and                s=(r_(X) ^(ECEF)+r_(y) ^(ECEF))^(1/2). such calculation                is iterated at least two times, preferably at least                three times to provide a converged solution, known as                the reduced latitude, that is calculated by:

$\beta = {\arctan\left\lbrack \frac{\left( {1 - f} \right)\sin\varphi}{\cos\varphi} \right\rbrack}$

-   -   -   -   wherein the altitude, h_(E), above Earth's surface is                calculated with the following equation:                h _(E)=(s·cos φ+r _(z) ^(ECEF) +e ² N sin φ)sin φ− N            -   wherein the radius of curvature in the vertical prime,                N, is found with

$N = \frac{R}{\left\lbrack {1 - {e^{2}\sin^{2}\varphi}} \right\rbrack^{1/2}}$

-   -   -   (vi) optionally updating said aerospace vehicle's propagated            position by using the inertial coordinates in a propagation            position and/or attitude calculation wherein said            calculation uses a Kalman Filter, an Extended Kalman Filter            and/or an Unscented Kalman Filter (typically the accuracy of            said aerospace vehicle's propagated position and/or attitude            is best if an Unscented Kalman Filter is used, with the next            best filter being an Extended Kalman Filter and/or a Kalman            Filter.

    -   b) determining the aerospace vehicle's pose estimation between        two points in time comprising:        -   (i) having an aerospace vehicle acquire, at a time from            Evening Civil Twilight to Morning Civil Twilight, at least            two images of the Earth at different times, each of said            images containing at least one common terrestrial light            feature;        -   (ii) comparing said two images to find at least one common            terrestrial light feature;        -   (iii) calculating the pose by first converting the image's            camera coordinates to normalized coordinates using the            following equations and method wherein the camera's            reference frame is defined with a first axis aligned with            the central longitudinal axis of the camera, a second axis,            that is a translation of said first axis and a normalization            of said camera's reference frame, a third axis that is a            rotation and translation of said second axis to the top left            corner of said image with the x-axis aligned with the local            horizontal direction and the y-axis points down the side of            the image from this top left corner and wherein said            rotation is aided by the camera's calibration matrix,            containing the focal lengths of the optical sensor, which            map to pixel lengths,

$X_{c} = \begin{bmatrix}x_{CAM} \\y_{CAM} \\z_{CAM}\end{bmatrix}$

$X_{n} = {\begin{bmatrix}x_{n} \\y_{n}\end{bmatrix} = \begin{bmatrix}{x_{CAM}/z_{CAM}} \\{y_{CAM}/z_{CAM}}\end{bmatrix}}$

$X_{p} = {\begin{bmatrix}x_{p} \\y_{p}\end{bmatrix} = {{\begin{bmatrix}f_{c} & 0 \\0 & f_{c}\end{bmatrix}\begin{bmatrix}x_{n} \\y_{n}\end{bmatrix}} + \begin{bmatrix}{n_{x}/2} \\{n_{y}/2}\end{bmatrix}}}$

-   -   -   (iv) calculating the essential matrix from the normalized            coordinates and then recovering the pose from the essential            matrix using the following equations, wherein the equation            for the epipolar constrain is defined as follows:            x _(n) ₁ ^(T)(t×Rx _(n) ₀ )=0            -   and said equation for the epipolar constraint is                rewritten as the following linear equation:                x _(n) ₁ ^(T) [t _(x) ]Rx _(n) ₀ =0            -   where

$\lbrack t\rbrack_{x} = \begin{bmatrix}0 & {- t_{z}} & t_{y} \\t_{z} & 0 & {- t_{x}} \\{- t_{y}} & t_{x} & 0\end{bmatrix}$

-   -   -   -   [t_(x)] is saying the translation vector should be                skewed (showing an operation) and [t]_(x) is showing                post-operation the skewed vector into a matrix.            -   the matrix [t]_(x) is redefined using the Essential                Matrix, E:                x _(n) ₁ ^(T) Ex _(n) ₀ =0                where                E=R[t] _(x)            -   and the Essential Matrix is scaled or unscaled. If                scaled, then the scale is known from the two images, and                reflects six degrees of freedom.            -   wherein other constraints on the Essential Matrix are                the following:                det(E)=0                2EE ^(T) E−tr(EE ^(T))E=0            -   or, when the epipolar constraint is applied to pixel                coordinates, then the Fundamental Matrix, F, is used:                x _(p) ₁ ^(T) Fx _(p) ₀ =0            -   said equation is then solved for the Fundamental Matrix                and the pose is recovered from the Essential and/or                Fundamental Matrices wherein said pose is defined as:                T=[R|t]

        -   (iv) combining the known absolute position and attitude of            the aerospace vehicle with the recovered pose to yield an            updated attitude and estimated position for the aerospace            vehicle wherein said combining step is achieved by using the            following equations wherein the attitude, C₁ at the second            image is defined by            C ₁ =C ₀ +R            -   wherein C₀ is preferably defined as zero if it is not                previously known; and inertial position corresponding to                the second image is found by adding the scaled change in                position, t, to the previous inertial position:                r ₁ =r ₀ +t.                Module and Aerospace Vehicle Comprising Same

For purposes of this specification, headings are not consideredparagraphs and thus this paragraph is Paragraph 0022 of the presentspecification. The individual number of each paragraph above and belowthis paragraph can be determined by reference to this paragraph'snumber. In this paragraph 0022, Applicants disclose a module comprisinga central processing unit programmed to determine an aerospace vehicle'sposition with respect to the Earth, an aerospace vehicle's poseestimation between two points in time and/or attitude with respect tothe Earth according to the method of Paragraph 0020.

Applicants disclose a module comprising a central processing unitprogrammed to determine an aerospace vehicle's position with respect tothe Earth, an aerospace vehicle's pose estimation between two points intime and/or attitude with respect to the Earth according to the methodof Paragraph 0021.

Applicants disclose the module of Paragraphs 0022 through 0023, saidmodule comprising an input/output controller, a random access memoryunit, and a hard drive memory unit, said input/output controller beingconfigured to receive a first digital signal, preferably said firstdigital signal comprises data from a sensor, more preferably said firstdigital signal comprises digitized imagery, and transmit a seconddigital signal comprising the updated aerospace vehicle's positionand/or attitude, to said central processing unit.

Applicants disclose an aerospace vehicle comprising:

-   -   a) a module according to any of Paragraphs 0022 through 0024;    -   b) a sensor pointed towards the earth, preferably said sensor        comprises a camera;    -   c) an internal and/or external power source for powering said        aerospace vehicle    -   d) an onboard central processing unit; and    -   e) a means to maneuver said aerospace vehicle, preferably said        means to maneuver said aerospace vehicle is selected from the        group consisting of a flight control surface, propeller,        thruster, electric propulsion, magnetorquer, momentum wheel,        more preferably said means to maneuver said aerospace vehicle is        selected from the group consisting of thruster, electric        propulsion, magnetorquer, momentum wheel.

When Applicants method is employed the position of the aerospace vehicleis supplied to the vehicle's guidance system and/or to one or moreindividuals who are guiding the aerospace vehicle so the aerospacevehicle may be guided in the manner desired to achieve the mission ofsaid aerospace vehicle.

EXAMPLES

The following examples illustrate particular properties and advantagesof some of the embodiments of the present invention. Furthermore, theseare examples of reduction to practice of the present invention andconfirmation that the principles described in the present invention aretherefore valid but should not be construed as in any way limiting thescope of the invention.

The aerospace vehicle pose and attitude determination method isimplemented for the Suomi NPP spacecraft in low Earth, sun-synchronousnear-polar orbit at an altitude of approximately 825 km. The spacecraftfeatures an Earth-pointing camera with a day/night light collection bandof 0.7 microns in the visible spectrum, and a ground field-of-view of1500 km. At 150-second time steps, and exactly over the Great Lakes andU.S. Midwest region, the Earth-pointing camera takes nighttimeterrestrial images. Using the pose determination method, the images arecompared with a known terrestrial lights database which is used as the“truth” dataset. Following comparison, the module computes an inertialorbital position vector and inertial orbital velocity vector for thespacecraft. Using the attitude determination method, the images arecompared with the same “truth” terrestrial lights database. Followingcomparison, the module computes the spacecraft's change of attitude interms of roll, pitch, and yaw, respectively.

The aerospace vehicle pose determination method is implemented for acommercial aviation flight across the U.S. from Cincinnati, Ohio, toPensacola, Florida. This route contains many major cities in its fieldof view during flight, such as Louisville, Kentucky; Nashville,Tennessee; and Atlanta, Georgia. The aircraft will be flying at 10,050meters at 290 meters per second during nighttime, with a camera in thevisible spectrum. Taking images every 15 minutes (900 seconds), anaccurate position can be found to verify the plane is still on thepre-determined flight plan in the case of GPS failure by comparing theimages with a known terrestrial lights database.

The aerospace vehicle pose and attitude determination method isimplemented for a scientific balloon flight carrying a payload and aground-pointing camera in the visible spectrum launching out of FortSumner, New Mexico, during a calm day. The balloon rises to a height of31,500 meters over a period of two hours. The balloon will stay ataltitude, fluctuating slightly during civil twilight, and descend over aperiod of minutes, when the balloon is separated from the payload andfalls back to Earth with a parachute deployment. The pose determinationmethod will be able to function during ascent and account for thechanging altitude, since the resolution of the camera will stayconstant, and still be able to determine a very accurate positionmeasurement. At the desired operating altitude, tracking position isessential so the balloon payload is not released over a populated area,which could cause harm to the population. The balloon would also be ableto track attitude, which is essential for the pointing of theinstrument, such as a telescope or sensor. For both pose and attitudedetermination, images are taken of terrestrial lights and compared witha known terrestrial lights database.

The aerospace vehicle pose and attitude determination method isimplemented for a re-entry vehicle with a ground-pointing camera in thevisible spectrum returning from Low Earth Orbit at 200,000 meters to theground, usually a water landing at zero meters. As with the balloon,this method is useful at determining the rapidly changing altitude thevehicle will experience, taking images right before and directly afterthe re-entry event, upon entering the sensible atmosphere. Terrestriallight matching with a known terrestrial lights database would act as aback-up or an alternative to the star tracker, GPS, and INS, that manyspace and air vehicles use for position and attitude, without having toswitch modes. The terrestrial light matching module would not functionduring the re-entry event itself due to high temperatures and lightexperienced by the vehicle entering the atmosphere at high speeds.

While the present invention has been illustrated by a description of oneor more embodiments thereof and while these embodiments have beendescribed in considerable detail, they are not intended to restrict orin any way limit the scope of the appended claims to such detail.Additional advantages and modifications will readily appear to thoseskilled in the art. The invention in its broader aspects is thereforenot limited to the specific details, representative apparatus andmethod, and illustrative examples shown and described. Accordingly,departures may be made from such details without departing from thescope of the general inventive concept.

What is claimed is:
 1. A method of determining an aerospace vehicle'sposition with respect to the Earth, comprising determining the aerospacevehicle's pose estimation between two points in time and/or attitudewith respect to the Earth wherein: a) determining the aerospacevehicle's position with respect to the Earth comprises: (i) having theaerospace vehicle acquire, at a time from Evening Civil Twilight toMorning Civil Twilight, an image of the Earth comprising at least oneterrestrial light feature; (ii) matching said at least one terrestriallight feature of the image with at least one feature of a terrestriallight data base; (iii) weighting said matched images; (iv) optionally,calculating a propagated position for said aerospace vehicle andchecking the result of said propagated position against the weighting;(v) using the time and the altitude that said image was taken to convertsaid weighted match into inertial coordinates; (vi) optionally updatingsaid aerospace vehicle's propagated position by using the inertialcoordinates in a propagation position and/or an attitude calculation;and/or b) determining the aerospace vehicle's pose estimation betweentwo points in time comprises: (i) having the aerospace vehicle acquire,at a time from Evening Civil Twilight to Morning Civil Twilight, atleast two images of the Earth at different times, each of said at leasttwo images containing at least one common terrestrial light feature;(ii) comparing said at least two images to find the at least one commonterrestrial light feature; (iii) calculating the aerospace vehicle'spose as follows: converting image coordinates of the at least two imagesthat were acquired by a camera to normalized coordinates; calculating anessential matrix from the normalized coordinates and then recovering thepose from the essential matrix; or converting image coordinates of theat least two images that were acquired by a camera to normalizedcoordinates; converting the normalized coordinates to pixel coordinates;calculating a fundamental matrix from the pixel coordinates and thenrecovering the pose; (iv) combining a known absolute position andattitude of the aerospace vehicle with the recovered pose to yield anupdated attitude and estimated position for the aerospace vehicle.
 2. Amethod of determining an aerospace vehicle's position with respect tothe Earth, determining the aerospace vehicle's pose estimation betweentwo points in time and/or attitude with respect to the Earth wherein: a)determining the aerospace vehicle's position with respect to the Earthcomprises: (i) having the aerospace vehicle acquire, at a known generalaltitude and at a time from Evening Civil Twilight to Morning CivilTwilight, an image of the Earth comprising at least one terrestriallight feature; (ii) matching, using Lowe's ratio test, said at least oneterrestrial light feature of the image with at least one feature of aterrestrial light data base; (iii) weighting, to a scale of one, saidmatched images; (iv) optionally, calculating a propagated position forsaid aerospace vehicle using at least one of a Kalman Filter, anExtended Kalman Filter and an Unscented Kalman Filter, and checking theresult of said propagated position against the weighting; (v) using thetime and the altitude that said image was taken at to convert saidweighted match into inertial coordinates by transforming a state vectorcontaining position and velocity from Earth-Centered-Earth-Fixed (ECEF)coordinates to Earth-Centered-Inertial (ECI) coordinates using thefollowing equations:r ^(ECI) =Rr ^(ECEF)v ^(ELI) =Rv ^(ECEF) +{dot over (R)}r ^(ECEF) $R = \begin{bmatrix}{{- \sin}\theta} & {{- \cos}\theta} & 0 \\{\cos\theta} & {{- \sin}\theta} & 0 \\0 & 0 & 0\end{bmatrix}${dot over (R)}=ω _(E) R where θ represents the Greenwich ApparentSidereal Time, measured in degrees and computed as follows:θ=[θ_(m)+Δψ cos(ε_(m)+Δε)]·mod(360°) where the Greenwich mean siderealtime is calculated as follows:θ_(m)=100.46061837+(36000.770053608)t+(0.000387933)t ²−(1/38710000)t ³where t represents the Terrestrial Time, expressed in 24-hour periodsand the Julian Day (JD):$t = \frac{{JD} - {2000{January}01^{d}12^{h}}}{36525}$ wherein the meanobliquity of the ecliptic is determined from:ε_(m)=23°26′21.″448−(46.″8150)t−(0.0″00059)t ²+(0.″001813)t ³ whereinthe nutations in obliquity and longitude involve the following threetrigonometric arguments:L=280.4665+(36000.7698)tL′=218.3165+(481267.8813)tΩ=125.04452−(1934.136261)t and, the nutations are calculated using thefollowing equations:Δψ=−17.20 sin ψ−1.32 sin(2L)−0.23 sin(2L′)+0.21 sin(2Ω)Δε=9.20 cos Ω+0.57 cos(2L)+0.10 cos(2L′)−0.09 cos(2Ω) then using, theequations for the position, r, and velocity, v, in the ECI frame tocalculate the position and velocity in the ECEF frame using thedimensions of the earth, when longitude is calculated from the ECEFposition by:$\psi = {\arctan\left\lbrack \frac{r_{y}^{ECEF}}{r_{x}^{ECEF}} \right\rbrack}$the geodetic latitude, φ_(gd), is calculated using Bowring's method:$\overset{¯}{\beta} = {\arctan\left\lbrack \frac{r_{z}^{ECEF}}{\left( {1 - f} \right)s} \right\rbrack}$$\varphi_{gd} = {\arctan\left\lbrack \frac{r_{z}^{ECEF} + {\frac{e^{2}\left( {1 - f} \right)}{\left( {1 - e^{2}} \right)}R\sin^{3}\beta}}{s - {e^{2}R\cos^{3}\beta}} \right\rbrack}$next the geocentric latitude is calculated from the geodetic,${\tan\varphi_{gc}} = {\frac{\left( {\frac{a_{e}\left( {1 - e^{2}} \right)}{\sqrt{1 - {e^{2}\sin^{2}\varphi_{gd}}}} + h_{gd}} \right)}{\left( {\frac{a_{e}}{\sqrt{1 - {e^{2}\sin^{2}\varphi_{gd}}}} + h_{gd}} \right)}\tan\varphi_{gd}}$where f is the flattening of the planet; e² is the square of the firsteccentricity, or e²=1−(1−f)²; and s=(r_(x) ^(ECEF)+r_(y) ^(ECEF))^(1/2)such calculation is iterated at least two times to provide a convergedsolution, known as the reduced latitude, that is calculated by:$\beta = {\arctan\left\lbrack \frac{\left( {1 - f} \right)\sin\varphi}{\cos\varphi} \right\rbrack}$wherein the altitude, h_(E), above Earth's surface is calculated withthe following equation:h _(E)=(s·cos φ+r _(z) ^(ECEF) +e ² N sin φ)sin φ− N wherein the radiusof curvature in the vertical prime, N, is found with$\overset{¯}{N} = \frac{R}{\left\lbrack {1 - {e^{2}\sin^{2}\varphi}} \right\rbrack^{1/2}}$(vi) optionally updating said aerospace vehicle's propagated position byusing the inertial coordinates in a propagation position and/or anattitude calculation wherein said calculation uses the at least one of aKalman Filter, an Extended Kalman Filter and an Unscented Kalman Filter;b) determining the aerospace vehicle's pose estimation between twopoints in time comprises: (i) having the aerospace vehicle acquire, at atime from Evening Civil Twilight to Morning Civil Twilight, at least twoimages of the Earth at different times, each of said at least two imagescontaining at least one common terrestrial light feature; (ii) comparingsaid at least two images to find the at least one common terrestriallight feature; (iii) calculating the aerospace vehicle's pose by firstconverting image coordinates of the at least two images that wereacquired by a camera to normalized coordinates using the followingequations and method, wherein a reference frame of the camera is definedwith a first axis aligned with the central longitudinal axis of thecamera, a second axis, that is a translation of said first axis and anormalization of said camera's reference frame, a third axis that is arotation and translation of said second axis to the top left corner ofsaid at least two images with the x-axis aligned with the localhorizontal direction and the y-axis pointing down on the side of the atleast two images from the top left corner, and wherein said rotation isaided by a calibration matrix of the camera, containing focal lengths ofan optical sensor, which maps to pixel lengths, $X_{c} = \begin{bmatrix}x_{CAM} \\y_{CAM} \\z_{CAM}\end{bmatrix}$ $X_{n} = {\begin{bmatrix}x_{n} \\y_{n}\end{bmatrix} = \begin{bmatrix}{x_{CAM}/z_{CAM}} \\{y_{CAM}/z_{CAM}}\end{bmatrix}}$ $X_{p} = {\begin{bmatrix}x_{p} \\y_{p}\end{bmatrix} = {{\begin{bmatrix}f_{c} & 0 \\0 & f_{c}\end{bmatrix}\begin{bmatrix}x_{n} \\y_{n}\end{bmatrix}} + \begin{bmatrix}{n_{x}/2} \\{n_{y}/2}\end{bmatrix}}}$ (iv) calculating an essential matrix from thenormalized coordinates and then recovering the pose from the essentialmatrix using the following equations, wherein the equation for theepipolar constraint is defined as follows:x _(n) ₁ ^(T)(t×Rx _(n) _(o) )=0 and said equation for the epipolarconstraint is rewritten as the following linear equation:x _(n) ₁ ^(T) [t _(x) ]Rx _(n) _(o) =0 where$\lbrack t\rbrack_{x} = \begin{bmatrix}0 & {- t_{z}} & t_{y} \\t_{z} & 0 & {- t_{x}} \\{- t_{y}} & t_{x} & 0\end{bmatrix}$ wherein [t_(x)] is saying the translation vector shouldbe skewed (showing an operation) and [t]_(x) is showing post-operationthe skewed vector into a matrix the matrix [t]_(x) is redefined usingthe Essential Matrix, E:x _(n) ₁ ^(T) Ex _(n) ₀ =0whereE=R[t] _(x) and the Essential Matrix is scaled or unsealed and ifscaled, then the scale is known from the two images, and reflects sixdegrees of freedom; wherein other constraints on the Essential Matrixare the following:det(E)=02EE ^(T) E−tr(EE ^(T))E=0 or, when the epipolar constraint is applied topixel coordinates, then a Fundamental Matrix, F, is used:x _(p) ₁ ^(T) Fx _(p) ₀ =0 said equation is then solved for theFundamental Matrix and the pose is recovered from the Essential and/orFundamental Matrices wherein said pose is defined as:T=[R|t] (iv) combining a known absolute position and attitude of theaerospace vehicle with the recovered pose to yield an updated attitudeand estimated position for the aerospace vehicle wherein said combiningstep is achieved by using the following equations wherein the attitude,C₁ at the second image is defined byC ₁ =C ₀ +R wherein C₀ and inertial position corresponding to the secondimage is found by adding the scaled change in position, t, to theprevious inertial position:r ₁ =r ₀ +t.
 3. A module comprising: a central processing unitprogrammed to determine an aerospace vehicle's position with respect tothe Earth, comprising determining the aerospace vehicle's poseestimation between two points in time and/or attitude with respect tothe Earth wherein: a) determining the aerospace vehicle's position withrespect to the Earth comprises: (i) having the aerospace vehicleacquire, at a time from Evening Civil Twilight to Morning CivilTwilight, an image of the Earth comprising at least one terrestriallight feature; (ii) matching said at least one terrestrial light featureof the image with at least one feature of a terrestrial light data base;(iii) weighting said matched images; (iv) optionally, calculating apropagated position for said aerospace vehicle and checking the resultof said propagated position against the weighting; (v) using the timeand the altitude that said image was taken to convert said weightedmatch into inertial coordinates; (vi) optionally updating said aerospacevehicle's propagated position by using the inertial coordinates in apropagation position and/or an attitude calculation; and/or b)determining the aerospace vehicle's pose estimation between two pointsin time comprises: (i) having the aerospace vehicle acquire, at a timefrom Evening Civil Twilight to Morning Civil Twilight, at least twoimages of the Earth at different times, each of said at least two imagescontaining at least one common terrestrial light feature; (ii) comparingsaid at least two images to find the at least one common terrestriallight feature; (iii) calculating the aerospace vehicle's pose asfollows: converting image coordinates of the at least two images thatwere acquired by a camera to normalized coordinates; calculating anessential matrix from the normalized coordinates and then recovering thepose from the essential matrix; or converting image coordinates of theat least two images that were acquired by a camera to normalizedcoordinates; converting the normalized coordinates to pixel coordinates;calculating a fundamental matrix from the pixel coordinates and thenrecovering the pose; (iv) combining a known absolute position andattitude of the aerospace vehicle with the recovered pose to yield anupdated attitude and estimated position for the aerospace vehicle.
 4. Amodule comprising: a central processing unit programmed to determine anaerospace vehicle's position with respect to the Earth, determining theaerospace vehicle's pose estimation between two points in time and/orattitude with respect to the Earth wherein: a) determining the aerospacevehicle's position with respect to the Earth comprises: (i) having theaerospace vehicle acquire, at a known general altitude and at a timefrom Evening Civil Twilight to Morning Civil Twilight, an image of theEarth comprising at least one terrestrial light feature; (ii) matching,using Lowe's ratio test, said at least one terrestrial light feature ofthe image with at least one feature of a terrestrial light data base;(iii) weighting, to a scale of one, said matched images; (iv)optionally, calculating a propagated position for said aerospace vehicleusing at least one of a Kalman Filter, an Extended Kalman Filter and anUnscented Kalman Filter, and checking the result of said propagatedposition against the weighting; (v) using the time and the altitude thatsaid image was taken at to convert said weighted match into inertialcoordinates by transforming a state vector containing position andvelocity from Earth-Centered-Earth-Fixed (ECEF) coordinates toEarth-Centered-Inertial (ECI) coordinates using the following equations:r ^(ECI) =Rr ^(ECEF)v ^(ELI) =Rv ^(ECEF) +{dot over (R)}r ^(ECEF) $R = \begin{bmatrix}{{- \sin}\theta} & {{- \cos}\theta} & 0 \\{\cos\theta} & {{- \sin}\theta} & 0 \\0 & 0 & 0\end{bmatrix}${dot over (R)}=ω _(E) R where θ represents the Greenwich ApparentSidereal Time, measured in degrees and computed as follows:θ=[θ_(m)+Δψ cos(ε_(m)+Δε)])mod(360° where the Greenwich mean siderealtime is calculated as follows:θ_(m)=100.46061837+(36000.770053608)t+(0.000387933)t ²−(1/38710000)t ³where t represents the Terrestrial Time, expressed in 24-hour periodsand the Julian Day (JD):$t = \frac{{JD} - {2000{January}01^{d}12^{h}}}{36525}$ wherein the meanobliquity of the ecliptic is determined from:ε_(m)=23°26′21.″448−(46.″8150)t−(0.0″00059)t ²+(0.″001813)t ³ whereinthe nutations in obliquity and longitude involve the following threetrigonometric arguments:L=280.4665+(36000.7698)tL′=218.3165+(481267.8813)tΩ=125.04452−(1934.136261)t and, the nutations are calculated using thefollowing equations:Δψ=−17.20 sin Ω−1.32 sin(2L)−0.23 sin(2L′)+0.21 sin(2Ω)Δε=9.20 cos Ω+0.57 cos(2L)+0.10 cos(2L′)−0.09 cos(2Ω) then using, theequations for the position, r, and velocity, v, in the ECI frame tocalculate the position and velocity in the ECEF frame using thedimensions of the earth, when longitude is calculated from the ECEFposition by:$\psi = {\arctan\left\lbrack \frac{r_{y}^{ECEF}}{r_{x}^{ECEF}} \right\rbrack}$the geodetic latitude, φ_(gd), is calculated using Bowring's method:$\overset{\_}{\beta} = {\arctan\left\lbrack \frac{r_{z}^{ECEF}}{\left( {1 - f} \right)s} \right\rbrack}$$\varphi_{gd} = {\arctan\left\lbrack \frac{r_{z}^{ECEF} + {\frac{e^{2}\left( {1 - f} \right)}{\left( {1 - e^{2}} \right)}R\sin^{3}\beta}}{s - {e^{2}R\cos^{3}\beta}} \right\rbrack}$next the geocentric latitude is calculated from the geodetic,${\tan\varphi_{gc}} = {\frac{\left( {\frac{a_{e}\left( {1 - e^{2}} \right)}{\sqrt{1 - {e^{2}\sin^{2}\varphi_{gd}}}} + h_{gd}} \right)}{\left( {\frac{a_{3}}{\sqrt{1 - {e^{2}\sin^{2}\varphi_{gd}}}} + h_{gd}} \right)}\tan\varphi_{gd}}$where f is the flattening of the planet; e² is the square of the firsteccentricity, or e²=1−(1−f)²; and s=(r_(x) ^(ECEF)+r_(y) ^(ECEF))^(1/2)such calculation is iterated at least two times to provide a convergedsolution, known as the reduced latitude, that is calculated by:$\beta = {\arctan\left\lbrack \frac{\left( {1 - f} \right)\sin\varphi}{\cos\varphi} \right\rbrack}$wherein the altitude, h_(E), above Earth's surface is calculated withthe following equation:h _(E)=(s·cos φ+r _(z) ^(ECEF) +e ² N sin φ)sin φ− N wherein the radiusof curvature in the vertical prime, N, is found with$\overset{\_}{N} = \frac{R}{\left\lbrack {1 - {e^{2}\sin^{2}\varphi}} \right\rbrack^{1/2}}$(vi) optionally updating said aerospace vehicle's propagated position byusing the inertial coordinates in a propagation position and/or anattitude calculation wherein said calculation uses the at least one of aKalman Filter, an Extended Kalman Filter and an Unscented Kalman Filter;b) determining the aerospace vehicle's pose estimation between twopoints in time comprises: (i) having the aerospace vehicle acquire, at atime from Evening Civil Twilight to Morning Civil Twilight, at least twoimages of the Earth at different times, each of said at least two imagescontaining at least one common terrestrial light feature; (ii) comparingsaid at least two images to find the at least one common terrestriallight feature; (iii) calculating the aerospace vehicle's pose by first,converting image coordinates of the at least two images that wereacquired by a camera to normalized coordinates using the followingequations and method, wherein a reference frame of the camera is definedwith a first axis aligned with the central longitudinal axis of thecamera, a second axis, that is a translation of said first axis and anormalization of said camera's reference frame, a third axis that is arotation and translation of said second axis to the top left corner ofsaid at least two images with the x-axis aligned with the localhorizontal direction and the y-axis pointing down on the side of the atleast two images from the top left corner, and wherein said rotation isaided by a calibration matrix of the camera, containing focal lengths ofan optical sensor, which maps to pixel lengths, $X_{c} = \begin{bmatrix}x_{CAM} \\y_{CAM} \\z_{CAM}\end{bmatrix}$ $X_{n} = {\begin{bmatrix}x_{n} \\y_{n}\end{bmatrix} = \begin{bmatrix}{x_{CAM}/z_{CAM}} \\{y_{CAM}/z_{CAM}}\end{bmatrix}}$ $X_{p} = {\begin{bmatrix}x_{p} \\y_{p}\end{bmatrix} = {{\begin{bmatrix}f_{c} & 0 \\0 & f_{c}\end{bmatrix}\begin{bmatrix}x_{n} \\y_{n}\end{bmatrix}} + \begin{bmatrix}{n_{x}/2} \\{n_{y}/2}\end{bmatrix}}}$ (iv) calculating an essential matrix from thenormalized coordinates and then recovering the pose from the essentialmatrix using the following equations, wherein the equation for theepipolar constraint is defined as follows:x _(n) ₁ ^(T)(t×Rx _(m) _(o) )=0 and said equation for the epipolarconstraint is rewritten as the following linear equation:x _(n) ₁ ^(T) [t _(x) ]Rx _(n) _(o) =0 where$\lbrack t\rbrack_{x} = \begin{bmatrix}0 & {- t_{z}} & t_{y} \\t_{z} & 0 & {- t_{x}} \\{- t_{y}} & t_{x} & 0\end{bmatrix}$ wherein [t_(x)] is saying the translation vector shouldbe skewed (showing an operation) and [t]_(x) is showing post-operationthe skewed vector into a matrix the matrix [t]_(x) is redefined usingthe Essential Matrix, E:x _(n) ₁ ^(T) Ex _(n) _(o) =0whereE=R[t] _(x) and the Essential Matrix is scaled or unscaled and ifscaled, then the scale is known from the two images, and reflects sixdegrees of freedom; wherein other constraints on the Essential Matrixare the following:det(E)=02EE ^(T) E−tr(EE ^(T))E=0 or, when the epipolar constraint is applied topixel coordinates, then a Fundamental Matrix, F, is used:x _(p) ₁ ^(T) Fx _(p) _(o) =0 said equation is then solved for theFundamental Matrix and the pose is recovered from the Essential and/orFundamental Matrices wherein said pose is defined as:T=[R|t] (iv) combining a known absolute position and attitude of theaerospace vehicle with the recovered pose to yield an updated attitudeand estimated position for the aerospace vehicle wherein said combiningstep is achieved by using the following equations wherein the attitude,C₁ at the second image is defined byC ₁ =C ₀ +R wherein C₀ and inertial position corresponding to the secondimage is found by adding the scaled change in position, t, to theprevious inertial position:r ₁ =r ₀ +t.
 5. The module of claim 3 further comprising: aninput/output controller, a random access memory unit, and a hard drivememory unit, said input/output controller being configured to receive afirst digital signal, and transmit a second digital signal comprisingthe updated aerospace vehicle's position and/or attitude, to saidcentral processing unit.
 6. The module of claim 5, wherein said firstdigital signal comprises data from a sensor.
 7. The module of claim 6,wherein said first digital signal comprises digitized imagery.
 8. Themodule of claim 4 further comprising: an input/output controller, arandom access memory unit, and a hard drive memory unit, saidinput/output controller being configured to receive a first digitalsignal, and transmit a second digital signal comprising the updatedaerospace vehicle's position and/or attitude, to said central processingunit.
 9. The module of claim 8, wherein said first digital signalcomprises data from a sensor.
 10. The module of claim 9, wherein saidfirst digital signal comprises digitized imagery.
 11. An aerospacevehicle comprising: a sensor pointed towards the earth; an internaland/or an external power source for powering said aerospace vehicle; anonboard central processing unit a means to maneuver said aerospacevehicle and a module comprising: an input/output controller, a randomaccess memory unit, and a hard drive memory unit, said input/outputcontroller being configured to receive a first digital signal, andtransmit a second digital signal comprising the updated aerospacevehicle's position and/or attitude, to said central processing unit, anda central processing unit programmed to determine an aerospace vehicle'sposition with respect to the Earth, comprising determining the aerospacevehicle's pose estimation between two points in time and/or attitudewith respect to the Earth wherein: a) determining the aerospacevehicle's position with respect to the Earth comprises: (i) having theaerospace vehicle acquire, at a time from Evening Civil Twilight toMorning Civil Twilight, an image of the Earth comprising at least oneterrestrial light feature; (ii) matching said at least one terrestriallight feature of the image with at least one feature of a terrestriallight data base; (iii) weighting said matched images; (iv) optionally,calculating a propagated position for said aerospace vehicle andchecking the result of said propagated position against the weighting;(v) using the time and the altitude that said image was taken to convertsaid weighted match into inertial coordinates; (vi) optionally updatingsaid aerospace vehicle's propagated position by using the inertialcoordinates in a propagation position and/or an attitude calculation;and/or b) determining the aerospace vehicle's pose estimation betweentwo points in time comprises: (i) having the aerospace vehicle acquire,at a time from Evening Civil Twilight to Morning Civil Twilight, atleast two images of the Earth at different times, each of said at leasttwo images containing at least one common terrestrial light feature;(ii) comparing said at least two images to find the at least one commonterrestrial light feature; (iii) calculating the aerospace vehicle'spose as follows: converting image coordinates of the at least two imagesthat were acquired by a camera to normalized coordinates; calculating anessential matrix from the normalized coordinates and then recovering thepose from the essential matrix; or converting image coordinates of theat least two images that were acquired by a camera to normalizedcoordinates; converting the normalized coordinates to pixel coordinates;calculating a fundamental matrix from the pixel coordinates and thenrecovering the pose; (iv) combining a known absolute position andattitude of the aerospace vehicle with the recovered pose to yield anupdated attitude and estimated position for the aerospace vehicle. 12.The aerospace vehicle according to claim 11, wherein said sensorcomprises a camera and said means to maneuver said aerospace vehiclecomprises at least one of a flight control surface, a propeller, athruster, an electric propulsion system, a magnetorquer, and a momentumwheel.
 13. An aerospace vehicle comprising: a sensor pointed towards theearth; an internal and/or an external power source for powering saidaerospace vehicle; an onboard central processing unit a means tomaneuver said aerospace vehicle and a module comprising: an input/outputcontroller, a random access memory unit, and a hard drive memory unit,said input/output controller being configured to receive a first digitalsignal, and transmit a second digital signal comprising the updatedaerospace vehicle's position and/or attitude, to said central processingunit, and a central processing unit programmed to determine an aerospacevehicle's position with respect to the Earth, determining the aerospacevehicle's pose estimation between two points in time and/or attitudewith respect to the Earth wherein: a) determining the aerospacevehicle's position with respect to the Earth comprises: (i) having theaerospace vehicle acquire, at a known general altitude and at a timefrom Evening Civil Twilight to Morning Civil Twilight, an image of theEarth comprising at least one terrestrial light feature; (ii) matching,using Lowe's ratio test, said at least one terrestrial light feature ofthe image with at least one feature of a terrestrial light data base;(iii) weighting, to a scale of one, said matched images; (iv)optionally, calculating a propagated position for said aerospace vehicleusing at least one of a Kalman Filter, an Extended Kalman Filter and anUnscented Kalman Filter, and checking the result of said propagatedposition against the weighting; (v) using the time and the altitude thatsaid image was taken at to convert said weighted match into inertialcoordinates by transforming a state vector containing position andvelocity from Earth-Centered-Earth-Fixed (ECEF) coordinates toEarth-Centered-Inertial (ECI) coordinates using the following equations:r ^(ECI) =Rr ^(ECEF)y ^(ECI) =Rv ^(ECEF) +{dot over (R)}r ^(ECEF) $R = \begin{bmatrix}{{- \sin}\theta} & {{- \cos}\theta} & 0 \\{\cos\theta} & {{- \sin}\theta} & 0 \\0 & 0 & 0\end{bmatrix}${dot over (R)}=ω _(E) R where θ represents the Greenwich ApparentSidereal Time, measured in degrees and computed as follows:θ=[θ_(m)+Δψ cos(ε_(m)+Δε)])·mod(360°) where the Greenwich mean siderealtime is calculated as follows:θ_(m)=100.46061837+(36000.770053608)t+(0.000387933)t ²−(1/38710000)t ³where t represents the Terrestrial Time, expressed in 24-hour periodsand the Julian Day (JD):$t = \frac{{JD} - {2000{January}{}01^{d}12^{h}}}{36525}$ wherein themean obliquity of the ecliptic is determined from:ε_(m)=23°26′21.″448−(46.″8150)t−(0.0″00059)t ²+(0.″001813)t ³ whereinthe nutations in obliquity and longitude involve the following threetrigonometric arguments:L=280.4665+(36000.7698)tL′=218.3165+(481267.8813)tΩ=125.04452−(1934.136261)t and, the nutations are calculated using thefollowing equations:Δψ=−17.20 sin Ω−1.32 sin(2L)−0.23 sin(2L′)+0.21 sin(2Ω)Δε=9.20 cos Ω+0.57 cos(2L)+0.10 cos(2L′)−0.09 cos(2Ω) then using, theequations for the position, r, and velocity, v, in the ECI frame tocalculate the position and velocity in the ECEF frame using thedimensions of the earth, when longitude is calculated from the ECEFposition by:$\psi = {\arctan\left\lbrack \frac{r_{c}^{ECEF}}{r_{x}^{ECEF}} \right\rbrack}$the geodetic latitude, φ_(gd), is calculated using Bowring's method:$\overset{\_}{\beta} = {\arctan\left\lbrack \frac{r_{z}^{ECEF}}{\left( {1 - f} \right)s} \right\rbrack}$$\varphi_{gd} = {\arctan\left\lbrack \frac{r_{z}^{ECEF} + {\frac{e^{2}\left( {1 - f} \right)}{\left( {1 - e^{2}} \right)}R\sin^{3}\beta}}{s - {e^{2}R\cos^{3}\beta}} \right\rbrack}$next the geocentric latitude is calculated from the geodetic,${\tan\varphi_{gc}} = {\frac{\left( {\frac{a_{e}\left( {1 - e^{2}} \right)}{\sqrt{1 - {e^{2}{\sin}^{2}\varphi_{gd}}}} + h_{gd}} \right)}{\left( {\frac{a_{e}}{\sqrt{1 - {e^{2}\sin^{2}\varphi_{gd}}}} + h_{gd}} \right)}\tan\varphi_{gd}}$where f is the flattening of the planet e² is the square of the firsteccentricity, or e²=1−(1−f)²; and s=(r_(x) ^(ECEF)+r_(y) ^(ECEF))^(1/2)such calculation is iterated at least two times to provide a convergedsolution, known as the reduced latitude, that is calculated by:$\beta = {\arctan\left\lbrack \frac{\left( {1 - f} \right)\sin\varphi}{\cos\varphi} \right\rbrack}$wherein the altitude, h_(E), above Earth's surface is calculated withthe following equation:h _(E)=(s·cos φ+r _(z) ^(ECEF) +e ² N sin φ)sin φ− N wherein the radiusof curvature in the vertical prime, N, is found with$\overset{\_}{N} = \frac{R}{\left\lbrack {1 - {e^{2}\sin^{2}\varphi}} \right\rbrack^{1/2}}$(vi) optionally updating said aerospace vehicle's propagated position byusing the inertial coordinates in a propagation position and/or anattitude calculation wherein said calculation uses the at least one of aKalman Filter, an Extended Kalman Filter and an Unscented Kalman Filter;b) determining the aerospace vehicle's pose estimation between twopoints in time comprises: (i) having the aerospace vehicle acquire, at atime from Evening Civil Twilight to Morning Civil Twilight, at least twoimages of the Earth at different times, each of said at least two imagescontaining at least one common terrestrial light feature; (ii) comparingsaid at least two images to find the at least one common terrestriallight feature; (iii) calculating the aerospace vehicle's pose by first,converting image coordinates of the at least two images that wereacquired by a camera to normalized coordinates using the followingequations and method, wherein a reference frame of the camera is definedwith a first axis aligned with the central longitudinal axis of thecamera, a second axis, that is a translation of said first axis and anormalization of said camera's reference frame, a third axis that is arotation and translation of said second axis to the top left corner ofsaid at least two images with the x-axis aligned with the localhorizontal direction and the y-axis pointing down on the side of the atleast two images from the top left corner, and wherein said rotation isaided by a calibration matrix of the camera, containing focal lengths ofan optical sensor, which maps to pixel lengths, $X_{c} = \begin{bmatrix}x_{CAM} \\y_{CAM} \\z_{CAM}\end{bmatrix}$ $X_{n} = {\begin{bmatrix}x_{n} \\y_{n}\end{bmatrix} = \begin{bmatrix}{x_{CAM}/z_{CAM}} \\{y_{CAM}/z_{CAM}}\end{bmatrix}}$ $X_{p} = {\begin{bmatrix}x_{p} \\y_{p}\end{bmatrix} = {{\begin{bmatrix}f_{c} & 0 \\0 & f_{c}\end{bmatrix}\begin{bmatrix}x_{n} \\y_{n}\end{bmatrix}} + \begin{bmatrix}{n_{x}/2} \\{n_{y}/2}\end{bmatrix}}}$ (iv) calculating an essential matrix from thenormalized coordinates and then recovering the pose from the essentialmatrix using the following equations, wherein the equation for theepipolar constraint is defined as follows:x _(n) ₁ ^(T)(t×Rx _(n) _(o) )=0 and said equation for the epipolarconstraint is rewritten as the following linear equation:x _(n) ₁ ^(T) [t _(x) ]Rx _(n) _(o) =0where $\lbrack t\rbrack_{x} = \begin{bmatrix}0 & {- t_{z}} & t_{y} \\t_{z} & 0 & {- t_{x}} \\{- t_{y}} & t_{x} & 0\end{bmatrix}$ wherein [t_(x)] is saying the translation vector shouldbe skewed (showing an operation) and [t]_(x) is showing post-operationthe skewed vector into a matrix the matrix [t]_(x) is redefined usingthe Essential Matrix, E:x _(n) ₁ ^(T) Ex _(n) _(o) =0whereE=R[t] _(x) and the Essential Matrix is scaled or unscaled and ifscaled, then the scale is known from the two images, and reflects sixdegrees of freedom; wherein other constraints on the Essential Matrixare the following:det(E)=02EE ^(T) E−tr(EE ^(T))E=0 or, when the epipolar constraint is applied topixel coordinates, then a Fundamental Matrix, F, is used:x _(p) ₁ ^(T) Fx _(p) _(o) =0 said equation is then solved for theFundamental Matrix and the pose is recovered from the Essential and/orFundamental Matrices wherein said pose is defined as:T=[R|t] (iv) combining a known absolute position and attitude of theaerospace vehicle with the recovered pose to yield an updated attitudeand estimated position for the aerospace vehicle wherein said combiningstep is achieved by using the following equations wherein the attitude,C₁ at the second image is defined byC ₁ =C ₀ +R wherein C₀ and inertial position corresponding to the secondimage is found by adding the scaled change in position, t, to theprevious inertial position:r ₁ =r ₀ +t.
 14. The aerospace vehicle according to claim 13, whereinsaid sensor comprises a camera and said means to maneuver said aerospacevehicle comprise at least one of a flight control surface, a propeller,a thruster, an electric propulsion system, a magnetorquer, and amomentum wheel.